Diffusion in Chemistry

Study Notes

Diffusion Overview

Diffusion is a process aimed at reducing free energy and concentration differences.
It occurs from areas of high concentration to low concentration, except in systems with miscibility gaps where diffusion moves toward high concentration.
Based on chemical potential, diffusion decreases energy by transitioning atoms from high to low chemical potential regions.
In cold-worked metals, diffusion occurs more rapidly due to factors like temperature, vacancies, grain boundaries, and anisotropy.

Atomic Mechanisms of Diffusion

Interstitial diffusion: Atoms navigate the spaces between larger atoms, forcing their way through the structure.
Substitutional movement: Atoms migrate through vacancies in the lattice.
Atomic vibrations at thermal energy of 3kT allow atoms to "jump" to adjacent vacancies, facilitating movement.

Temperature Effects on Diffusion

Higher temperatures lead to increased equilibrium vacancy concentrations, enhancing available space for diffusion.
The amplitude and energy of atomic vibrations rise, allowing atoms to occupy adjacent sites more easily.
Smaller atoms predominantly occupy interstitial sites, with many sites remaining empty.
Atomic jumps occur when thermal energy surpasses the strain energy barrier.

Interstitial Diffusion Dynamics

Interstitial diffusion operates as a random jump process due to numerous empty sites surrounding each atom.
Simple models show that B atoms occupy interstitial sites with six surrounding empty sites.
The jumping rate of B atoms (ΓB) affects the net flux of atoms between planes based on concentration differences.

Fick's First Law of Diffusion

Fick's First Law relates the diffusion flux (J) to the concentration gradient (∂C/∂x).
The intrinsic diffusivity (DB), with units [m²/s], represents how concentration changes over time.
Flux and concentration can be any consistent units like atoms or moles, enhancing flexibility in calculations.

Diffusivity Considerations

In random atomic jumps, DB remains constant regardless of concentration, applicable for simple cubic lattices.
For non-cubic lattices like hexagonal structures, diffusion rates vary directionally due to unequal jump probabilities.
Random jumping assumptions often do not hold in real alloys, necessitating adjustments for compositional variations in D.

Values of Diffusivity

At 1000°C, diffusivity for carbon in fcc-Fe varies with concentration:
- DC = 2.5 x 10⁻¹¹ m²/s at 0.15 wt% C.
- DC = 7.7 x 10⁻¹¹ m²/s at 1.4 wt% C, highlighting that higher concentration facilitates diffusion by straining the lattice.

Jump Frequency Calculations

For carbon in γ-Fe at 1000°C, the jump frequency can be estimated using the lattice parameter (~0.37 nm) and jump distance (0.26 nm).
With D at 2.5 x 10⁻¹¹ m²/s, the jump frequency (Γ) is calculated to be approximately 2 x 10⁹ jumps/s.
Despite high atom vibration frequencies (~10¹³), only a limited number of jumps (1 in 10⁴) result in successful site transfers.

Random Walk of a Single Atom

The concept of a random walk emphasizes that each atomic jump is random and independent, contributing to overall diffusion behavior.

Description

Explore the fundamentals of diffusion in this quiz. Learn how diffusion occurs to reduce free energy and the behavior of substances as they move from high to low concentration. Understand the factors that influence diffusion, including temperature and chemical potential.